Question: Simplify the following expression: $a = \dfrac{t^2 + 5t - 24}{t + 8} $
Answer: First factor the polynomial in the numerator. $ t^2 + 5t - 24 = (t + 8)(t - 3) $ So we can rewrite the expression as: $a = \dfrac{(t + 8)(t - 3)}{t + 8} $ We can divide the numerator and denominator by $(t + 8)$ on condition that $t \neq -8$ Therefore $a = t - 3; t \neq -8$